Sec 3.1 Polynomials and Their Graphs (std MA 6.0)

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Sec 3.1 Polynomials and Their Graphs (std MA 6.0)

• Objectives
• To determine left and right end behavior of a
  polynomial.
• To find the zeros of a polynomial by factoring.

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Determining left and right end behavior of a
polynomial.

• To determine the left and right end behavior of a
  polynomial we need to look at two things.
• The leading coefficient of the function.
• The degree of the function.
• Recall xn and xn.

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We can summarize our findings in a table.
y xn where n is even y -xn where n is even y xn where n is odd y -xn where n is odd

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Ex 1. For the following graphs determine the left
and right behavior of the graph.

1. y 3x24x-6
2. y -3x35x-8
3. y x5-4x35
4. y -2x4 x3-2x26x-18
5. y (x-2)(x1)(x2)

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Zeros of a Polynomial Function

• If P is a polynomial and c is a real number, then
  the following are true.
• c is a zero of P.
• x c is a solution of the equation P(x) 0.
• x c is a factor of P(x).
• x c is an x-intercept of the graph of P.

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Ex 1. Find the zeros of P(x) x2 x 6 by
factoring.
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Ex 2. Find the zeros by factoring.

• P(x) x3 3x2 10x
• b) P(x) x4 x3 8x - 8

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Ex 3. Find the zeros and determine the end
behavior of each graph.
a)
b)
c)
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Class Work

• Find the zeros and determine the end behavior.
• 1. P(x) -2x(x 6)
• 2. P(x) 9x2 18x -7
• 3. P(x) (x-3)(x4)(x-8)(x7)
• 4. P(x) 2x3 - 4x2 16x

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HW 1 p262 1-3(describe the transformations) 5-10
all, 11-35 odd (find zeros and find end behavior)